$g(t) = -2t^{2}+5t-2(h(t))$ $h(n) = 3n+4(f(n))$ $f(x) = 2x$ $ g(h(1)) = {?} $
Explanation: First, let's solve for the value of the inner function, $h(1)$ . Then we'll know what to plug into the outer function. $h(1) = (3)(1)+4(f(1))$ To solve for the value of $h$ , we need to solve for the value of $f(1)$ $f(1) = (2)(1)$ $f(1) = 2$ That means $h(1) = (3)(1)+(4)(2)$ $h(1) = 11$ Now we know that $h(1) = 11$ . Let's solve for $g(h(1))$ , which is $g(11)$ $g(11) = -2(11^{2})+(5)(11)-2(h(11))$ To solve for the value of $g$ , we need to solve for the value of $h(11)$ $h(11) = (3)(11)+4(f(11))$ To solve for the value of $h$ , we need to solve for the value of $f(11)$ $f(11) = (2)(11)$ $f(11) = 22$ That means $h(11) = (3)(11)+(4)(22)$ $h(11) = 121$ That means $g(11) = -2(11^{2})+(5)(11)+(-2)(121)$ $g(11) = -429$